Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-2y &= 4 \\ -3x+2y &= -8\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-3x = -2y-8$ Divide both sides by $-3$ to isolate $x$ $x = {\dfrac{2}{3}y + \dfrac{8}{3}}$ Substitute this expression for $x$ in the first equation. $-5({\dfrac{2}{3}y + \dfrac{8}{3}}) - 2y = 4$ $-\dfrac{10}{3}y - \dfrac{40}{3} - 2y = 4$ Simplify by combining terms, then solve for $y$ $-\dfrac{16}{3}y - \dfrac{40}{3} = 4$ $-\dfrac{16}{3}y = \dfrac{52}{3}$ $y = -\dfrac{13}{4}$ Substitute $-\dfrac{13}{4}$ for $y$ in the top equation. $-5x-2( -\dfrac{13}{4}) = 4$ $-5x+\dfrac{13}{2} = 4$ $-5x = -\dfrac{5}{2}$ $x = \dfrac{1}{2}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = -\dfrac{13}{4}$.